A note on global attractivity in models of hematopoiesis
We consider the delay differential equations \(P'(t) = \frac{{\beta _0 \theta ^n [P(t - \tau )]^j }}{{\theta ^n + [P(t - \tau )]^n }} - \delta P(t),{\rm{ }}j = 0,1,\) which were proposed by Mackey and Glass as a model of blood cell production. We suggest new conditions sufficient for th...
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| Date: | 1998 |
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| Main Authors: | , |
| Format: | Article |
| Language: | English |
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Institute of Mathematics, NAS of Ukraine
1998
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| Online Access: | https://umj.imath.kiev.ua/index.php/umj/article/view/4967 |
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| Journal Title: | Ukrains’kyi Matematychnyi Zhurnal |
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Ukrains’kyi Matematychnyi Zhurnal| _version_ | 1860511154527272960 |
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| author | Gopalsamy, К. Гопалсамі, К. |
| author_facet | Gopalsamy, К. Гопалсамі, К. |
| author_sort | Gopalsamy, К. |
| baseUrl_str | https://umj.imath.kiev.ua/index.php/umj/oai |
| collection | OJS |
| datestamp_date | 2020-03-18T21:21:24Z |
| description | We consider the delay differential equations \(P'(t) = \frac{{\beta _0 \theta ^n [P(t - \tau )]^j }}{{\theta ^n + [P(t - \tau )]^n }} - \delta P(t),{\rm{ }}j = 0,1,\) which were proposed by Mackey and Glass as a model of blood cell production. We suggest new conditions sufficient for the positive equilibrium of the equation considered to be a global attractor. In contrast to the Lasota-Wazewska model, we establish the existence of the number δj = δj(n, τ) > 0 such that the equilibrium of the equation under consideration is a global attractor for all δ ε (0, δj] independently of β0 and θ. |
| first_indexed | 2026-03-24T03:08:23Z |
| format | Article |
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| id | umjimathkievua-article-4967 |
| institution | Ukrains’kyi Matematychnyi Zhurnal |
| keywords_txt_mv | keywords |
| language | English |
| last_indexed | 2026-03-24T03:08:23Z |
| publishDate | 1998 |
| publisher | Institute of Mathematics, NAS of Ukraine |
| record_format | ojs |
| resource_txt_mv | umjimathkievua/1d/76fdb8718778d461371fffbbe5d2ee1d.pdf |
| spelling | umjimathkievua-article-49672020-03-18T21:21:24Z A note on global attractivity in models of hematopoiesis Про глобальні атрактори в моделі відтворення кров'яних тілець Gopalsamy, К. Гопалсамі, К. We consider the delay differential equations \(P'(t) = \frac{{\beta _0 \theta ^n [P(t - \tau )]^j }}{{\theta ^n + [P(t - \tau )]^n }} - \delta P(t),{\rm{ }}j = 0,1,\) which were proposed by Mackey and Glass as a model of blood cell production. We suggest new conditions sufficient for the positive equilibrium of the equation considered to be a global attractor. In contrast to the Lasota-Wazewska model, we establish the existence of the number δj = δj(n, τ) > 0 such that the equilibrium of the equation under consideration is a global attractor for all δ ε (0, δj] independently of β0 and θ. Розглядаються диференціальні рівняння з запізненням по $$P'(t) = \frac{{\beta _0 \theta ^n [P(t - \tau )]^j }}{{\theta ^n + [P(t - \tau )]^n }} - \delta P(t),{\rm{ }}j = 0,1,$$ що були запропоновані Маккейом та Глассом як модель процесу відтворення червоних кров'яних тілець. Запропоновано нові умови, достатні для того, щоб позитивна точка рівноваги наведеного рівняння була глобальним атрактором. На відміну від моделі Ласоти - Важевської встановлено існування числа $δ_j = δ_j(n, τ) > 0$ такого, що точка рівноваги вказаного рівняння є глобальним трактором для всіх $δ ε (0, δj]$ незалежно від $β_0$ та $θ$. Institute of Mathematics, NAS of Ukraine 1998-01-25 Article Article application/pdf https://umj.imath.kiev.ua/index.php/umj/article/view/4967 Ukrains’kyi Matematychnyi Zhurnal; Vol. 50 No. 1 (1998); 5–12 Український математичний журнал; Том 50 № 1 (1998); 5–12 1027-3190 en https://umj.imath.kiev.ua/index.php/umj/article/view/4967/6633 https://umj.imath.kiev.ua/index.php/umj/article/view/4967/6634 Copyright (c) 1998 Gopalsamy К. |
| spellingShingle | Gopalsamy, К. Гопалсамі, К. A note on global attractivity in models of hematopoiesis |
| title | A note on global attractivity in models of hematopoiesis |
| title_alt | Про глобальні атрактори в моделі відтворення кров'яних тілець |
| title_full | A note on global attractivity in models of hematopoiesis |
| title_fullStr | A note on global attractivity in models of hematopoiesis |
| title_full_unstemmed | A note on global attractivity in models of hematopoiesis |
| title_short | A note on global attractivity in models of hematopoiesis |
| title_sort | note on global attractivity in models of hematopoiesis |
| url | https://umj.imath.kiev.ua/index.php/umj/article/view/4967 |
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